Section 26. If the offer so made by either party is accepted by the other, it shall establish the annual compensation to be thereafter paid, as if it had been established by a judgment in a civil action, if a memorandum of such offer and acceptance and of the agreement, signed by the respective parties or by persons authorized by them, is filed and recorded in the office of the clerk of the court in which the former judgment was rendered, with a note of reference on the record of the former judgment to the book in which the agreement is recorded.